Bicycle chains accumulate gunk which tends to be composed of dirt from the environment (dirt kicked up from the front wheel as well as abraded rim material if you have rim brakes) and abraded material from the chain and the cogs/chainrings, all held in colloidal suspension with the lubricant grease from the chain.
1) Fully-encased chain guard will reduce the environmental source of gunk but you'd still get thick/black grease from the wear and tear on the chain itself. Furthermore, chain guards make maintenance and cleaning more difficult. On the positive side, you don't worry about what you can't see.
1a) Bicycles with oil bath chaincases used to exist, that would drag the chain through oil - much like a wet sump on cars. This would cause constant lubrication, decreasing wear. However, I imagine that they would leak like crazy and that the oil - much like auto oil - would be black, dirty, and messy. The system would also be heavy. For these and many other reasons, they haven't been produced in almost 80 years.
2) A full front fender with mud-guard will help reduce the amount of debris kicked up from the front wheel onto the chain. Added bonus, it'll keep your toes cleaner/drier in the rain as well.
3) Single-speeds use thicker chains and because they don't have to cross-chain, there's less lateral wear on the chains from chain/cog abrasion. Less wear, less gunk. Since most chaincases/chainguards aren't derailleur compatible, you'd want to look into the next solution as an alternative.
4) Internal-gear-hub has the advantage of single-speeds with the advantage of changing gears. If you want to remain with chain technology, a single speed or IGH with fully enclosed chain is the winner.
5) Leaving chain technology behind, your the next best is a belt drive. Belt drive bikes will give off a black powder residue (which is essentially worn belt) but don't collect gunk as they don't use lubricants.
6) Much rarer in the United States are shaft drive bicycles. Because these use a fully-enclosed drive mechanism (which still needs lubricating, by the way), there's no chain gunk.
In reality, people are in either: Camp A) ignore the chain gunk and rarely clean their chains; or Camp B) get obsessive about cleaning their chains and get all sorts of accoutrements to do so. Since you seem to not enjoy cleaning your chain, I'd just stick with Camp A, ignore the chain, and just replace your chain and cogs when time comes. Getting a chain guard means you won't have to look at your chain and won't worry.